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Superconductor Science and Technology

Design methodology of single-flux-quantum flip-flops composed of both 0- and π-shifted Josephson junctions

Yuki Yamanashi, Sotaro Nakaishi, Akira Sugiyama, Naoki Takeuchi, Nobuyuki Yoshikawa

Published Aug 2, 2018• 37 citations
Publisher

Abstract

A methodology for designing single-flux-quantum (SFQ) flip-flops composed of both conventional (0-) and π -shifted Josephson junctions is investigated. We investigated the implementation of a storage loop, which can store flux quantum and is indispensable to express binary logic states in superconductor logic circuits. As all SFQ flip-flops have storage loops, the investigated design methodology can be applied to their design. We designed several SFQ flip-flops composed of 0- and π -shifted Josephson junctions using the investigated design methodology. The performances of the designed SFQ flip-flops were quantitatively evaluated by using an analog circuit simulator which we developed. We confirmed the correct operation of various SFQ flip-flops composed of 0- and π -shifted Josephson junctions with wide operating margins. Moreover, we observed that the investigated design methodology is suitable for SFQ flip-flops with complementary outputs because a storage loop composed of both 0- and π -shifted Josephson junctions has a symmetric structure and the complementary output function can be realized by using the storage loop. Our investigation indicates that the number of Josephson junctions and static power consumption of a non-destructive read-out flip-flop with complementary outputs (NDROC) can be reduced to less than half of those of the conventional NDROC, which has two storage loops composed of 0-Josephson junctions, to realize the complementary output function. The investigated design methodology is expected to be applied to not only SFQ circuits but also other superconducting logic circuits and novel reconfigurable logic devices using programmable 0- π Josephson junctions.

DOI
10.1088/1361-6668/aad78d

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A methodology for designing single-flux-quantum (SFQ) flip-flops composed of both conventional (0-) and π -shifted Josephson junctions is investigated. We investigated the implementation of a storage loop, which can store flux quantum and is indispensable to express binary logic states in superconductor logic circuits. As all SFQ flip-flops have storage loops, the investigated design methodology can be applied to their design. We designed several SFQ flip-flops composed of 0- and π -shifted Josephson junctions using the investigated design methodology. The performances of the designed SFQ flip-flops were quantitatively evaluated by using an analog circuit simulator which we developed. We confirmed the correct operation of various SFQ flip-flops composed of 0- and π -shifted Josephson junctions with wide operating margins. Moreover, we observed that the investigated design methodology is suitable for SFQ flip-flops with complementary outputs because a storage loop composed of both 0- and π -shifted Josephson junctions has a symmetric structure and the complementary output function can be realized by using the storage loop. Our investigation indicates that the number of Josephson junctions and static power consumption of a non-destructive read-out flip-flop with complementary outputs (NDROC) can be reduced to less than half of those of the conventional NDROC, which has two storage loops composed of 0-Josephson junctions, to realize the complementary output function. The investigated design methodology is expected to be applied to not only SFQ circuits but also other superconducting logic circuits and novel reconfigurable logic devices using programmable 0- π Josephson junctions.
We designed several single flux quantum (SFQ) flip-flops and logic gates composed of Josephson junctions (JJs) and π-shifted JJs (π-JJs) to quantitatively evaluate effectiveness of introduction of π-JJs into the SFQ logic circuit. One-output flip-flops and logic gates were designed on the basis of the circuit design methodology we built for the SFQ circuit containing π-JJs. The designed flip-flops and logic gates have wide operating margins, the dc-bias margins of larger than ±30%, and device parameter margins of ±18%, though the static power consumption are reduced compared to conventional ones composed of JJs. We found that the difference in the critical current density between JJs and π-JJs does not affect the operating margins of the SFQ flip-flop composed of JJs and π-JJs. We devised a circuit structure of the delay flip-flop with complementary outputs composed of JJs and π-JJs (π-DFFC). The analog circuit simulation shows the dc-bias margin of the π-DFFC is larger than ±33%. These results indicate that the large-scale SFQ logic circuit system can be implemented using the flip-flops and logic gates containing π-JJs.
We report on the functionality of a Nb-based superconducting single flux quantum (SFQ) toggle flip-flop (TFF) circuit, comprising a complementary superconductor–ferromagnet–superconductor (SFS) Josephson π-junction. The SFS junction was used as a phase shifting element inserted in the storage loop of the TFF. The fabricated circuits demonstrated correct functionality with the operation parameter ranges of ± 20%. The application of SFS π-junctions makes the SFQ circuits very compact, may substantially improve their stability, and may also be suitable for integration with Josephson quantum circuits (qubits).
We report optimization of half-flux-quantum (HFQ) circuits composed of SQUIDs containing conventional Josephson junctions and π-shift magnetic Josephson junctions. The SQUID can act as a Josephson junction with an extremely small critical current and be easily switched by a weak driving force with the assistance of the circulating current that is induced due to the π-shift and quantization conditions. It leads to a drastic reduction of both static and dynamic power consumption. However, the parameter margins of the HFQ circuits obtained so far is narrow compared with conventional single-flux-quantum circuits. Since HFQ circuits use many circuit elements and require the two junctions in the SQUID to switch alternately and symmetrically, circuit parameter optimization is much more difficult. In this study, we developed an optimization tool for HFQ circuits, including operation judgment and margin calculation. We improved the critical margin of the HFQ Josephson transmission line to 39%. We also optimized the HFQ splitter, confluence buffer, and D flip-flop. We discuss design guidelines for HFQ circuits based on our systematic exploration of the optimized circuit parameter sets. We suggest that the optimized loop inductances are around 0.5 and 1.5 of Φ0/2 for data transmission and storage, respectively.
Novel reconfigurable superconductive single flux quantum (SFQ) logic devices, the functions of which can be dynamically reconfigured by inputting control signals, have been investigated. The characteristics of single flux quantum circuits can be easily modulated by applying currents or magnetic fields because of the high sensitivity of superconductive circuits. We investigated several design approaches for the realization of dynamically reconfigurable SFQ logic devices. We employed direct current injection to the logic gate using a non-destructive read-out flip-flop. By changing the internal state of the non-destructive read-out flip-flop, the logic function can be dynamically reconfigured. We have designed and tested a dynamically reconfigurable Josephson transmission line (JTL)/delay flip-flop (DFF) circuit. The measured dc bias margin was 72.5-107.2%. Furthermore, we have demonstrated the operation of a variable bit-length shift register, composed of the dynamically reconfigurable JTL/DFF circuits. The investigated design approach can be applied to more sophisticated dynamically reconfigurable single flux quantum logic gates.
We present a concept of an advanced rapid single-flux-quantum (RSFQ) logic circuit family using the combination of 0-shifted and π-shifted Josephson junctions. A π-shift in the current-phase relationship can be obtained in several types of Josephson junctions, such as Josephson junctions containing a ferromagnet barrier layer, depending on its thickness and temperature. We use a superconducting quantum interference devices composed of a pair of 0- and π-shifted Josephson junctions (0-π SQUIDs) as a basic circuit element. Unlike the conventional RSFQ logic, bistability is obtained by spontaneous circular currents without using a large superconductor loop, and the state can be flipped by smaller driving currents. These features lead to energy- and/or space-efficient logic gates. In this paper, we show several example circuits where we represent signals by flips of the states of a 0-π SQUID. We obtained successful operation of the circuits from numerical simulation.
We have found that the size of some rapid single-flux quantum (RSFQ) logic cells based on conventional 0-type Josephson junctions can be significantly reduced by using a π-type junction as a phase shifter in passive (nonswitching) mode. In comparison with the recently suggested active (switching) π-junctions mode, the passive mode offers much greater operation margins for their critical current Icπ. This gives π-junctions a chance to be implemented in RSFQ designs in the near future. As an example, we have simulated the operation of a toggle flip flop with zero-geometrical inductance of the fluxon storage loop. Simulations show that the parametric inductance of the π-junction and its normal resistance Rn form a low-pass filter, which sets the low limit for π-junctions IcπRn product, but offers a wide range of variations of the other parameters. The possible reduction of RSFQ cell size by using π-junctions opens the way to scale superconducting logic circuits down to the submicron dimensions.